You of course realize that in expressing good intentions, you are not alone, and certainly not first. The devil is in the details. Parsing Mathematica expressions into an intermediate form (like a Lisp symbolic expression) is the easy part.
Here's a detail that came up in another mailing list. What is Infinity or Inf in Mma? Is it the same as in your favorite other CAS? Or in your favorite text? Mma says 1/Inf = 0. It also says -1/Inf =0. From which we might conclude that 1=-1. Do we have to get around this? If so, how? If you have a system that has a more nuanced version of infinity, what do you do? There are other similar issues. Another point -- that if two CAS come up with the "same" answer, it must be right, is wishful thinking. In certain simple domains I would treat equal results as strongly confirmatory. There used to be a list of system-independent bugs -- caused by common simplistic thinking, where mathematics taught in high school is used as the basis for manipulating more sophisticated ideas. Sorry to provide a bit more rain on your parade. Have fun with the easy parts and see how far you can get with the hard parts! RJF On Friday, July 10, 2020 at 11:30:51 AM UTC-7, Rocky Bernstein wrote: > > Ok. Something to consider is rendering to Mathematica output. (And then > doing the same thing for Sage.) > > On Fri, Jul 10, 2020 at 1:37 PM Fredrik Johansson <fredrik....@gmail.com > <javascript:>> wrote: > >> I will just mention http://fungrim.org/grim/ which is somewhat related >> to the present discussion. >> >> This is an attempt to design a symbolic formula language that is easy to >> parse and has well-defined semantics. Key points: >> >> * Can be used within Python (and other languages) without special syntax >> * Expressly designed to describe mathematical objects and not for >> reflection (manipulation of symbolic expressions is meant to be done in the >> environment, e.g. Python, not from within the symbolic expression language) >> * Expressions are inert by default (there is no automatically-enforced >> pseudo-canonical form, and any form of evaluation or rewriting must be >> invoked explicitly by the user) >> * Evaluation and simplification is subject to a rigorous assumptions >> system >> * There is an explicit distinction between symbolic variables and >> polynomial indeterminates >> * Real numbers are mathematical real numbers >> * Functions are mathematical functions, with well-defined and consistent >> behavior at "exceptional points" >> >> The specification is still far from complete and the implementation still >> has a long way to go, but I'm working on it :-) >> >> I'm using it with some success to build http://fungrim.org/. Thanks to >> the strong semantics, it is possible to do automated randomized testing of >> the formulas and their assumptions. To illustrate: >> >> >>> formula = Equal(Gamma(x+1), x*Gamma(x)) >> >>> formula.test(variables=[x], assumptions=Element(x, CC)) >> {x: -3} ... True >> {x: 8} ... True >> {x: 0} ... False >> Traceback (most recent call last): >> ... >> ValueError >> >> (Gamma(0+1) = 0*Gamma(0) is not a true identity.) With correct >> assumptions, excluding the poles: >> >> >>> formula.test(variables=[x], assumptions=Element(x, SetMinus(CC, >> ZZLessEqual(0)))) >> {x: Sqrt(2)} ... Unknown >> {x: Mul(Mul(2, Pi), ConstI)} ... Unknown >> {x: Div(Mul(3, Pi), 2)} ... Unknown >> {x: Neg(Div(1, 2))} ... True >> {x: Div(1, 2)} ... True >> {x: Add(Sqrt(2), 1)} ... Unknown >> {x: Add(1, ConstI)} ... Unknown >> ... >> {x: Sub(Pi, ConstI)} ... Unknown >> {x: Sub(Sqrt(2), 1)} ... Unknown >> {x: 64} ... True >> {x: 255} ... Unknown >> {x: 7} ... True >> Passed 100 instances (25 True, 75 Unknown, 0 False) >> {'True': 25, 'Unknown': 75, 'False': 0, 'Total': 100} >> >> Fredrik >> >> On Friday, July 10, 2020 at 5:21:07 PM UTC+2 rocky.b...@gmail.com wrote: >> >>> Ok. This is on my back-burner list of things to get to. >>> >>> It is something I would like to do, and think I could do reasonably >>> well, but I never know if I'll have the free time. >>> >>> And if someone else wants to take the lead, I'll be happy to share what >>> I know on the compiler/transpiler end and contribute. >>> >>> Also, if there is funding for this effort, then it will most likely get >>> done. >>> >>> >>> >>> On Fri, Jul 10, 2020 at 10:52 AM kcrisman <kcri...@gmail.com> wrote: >>> >>>> >>>> >>>> >>>> Clearly, adding the ability to parse some Mathematica code fits well >>>>> into that goal. If nothing else, it could be a helpful step in >>>>> converting >>>>> existing Mathematica user code so that it can work in Sage, and >>>>> that's part of being a viable alternative. >>>>> >>>> >>>> This is an important point that I am sorry we did not mention earlier; >>>> thanks, William. I have definitely had many requests for such an >>>> automated >>>> tool in the past from colleagues with a lot of Mma stuff. >>>> >>>> -- >>>> >>> You received this message because you are subscribed to a topic in the >>>> Google Groups "sage-devel" group. >>>> To unsubscribe from this topic, visit >>>> https://groups.google.com/d/topic/sage-devel/z3XBhQOCh9E/unsubscribe. >>>> >>> To unsubscribe from this group and all its topics, send an email to >>>> sage-devel+...@googlegroups.com. >>>> To view this discussion on the web visit >>>> https://groups.google.com/d/msgid/sage-devel/8dd1a617-6bcc-40e3-a1c7-89efb2927597o%40googlegroups.com >>>> >>>> <https://groups.google.com/d/msgid/sage-devel/8dd1a617-6bcc-40e3-a1c7-89efb2927597o%40googlegroups.com?utm_medium=email&utm_source=footer> >>>> . >>>> >>> -- >> You received this message because you are subscribed to a topic in the >> Google Groups "sage-devel" group. >> To unsubscribe from this topic, visit >> https://groups.google.com/d/topic/sage-devel/z3XBhQOCh9E/unsubscribe. >> To unsubscribe from this group and all its topics, send an email to >> sage-...@googlegroups.com <javascript:>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sage-devel/050a44ed-e31b-4ddb-8687-fc9dcd53e3c1n%40googlegroups.com >> >> <https://groups.google.com/d/msgid/sage-devel/050a44ed-e31b-4ddb-8687-fc9dcd53e3c1n%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. 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